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Cardinality | 8 (octatonic) |
---|---|
Pitch Class Set | {0,1,2,3,4,7,9,10} |
Forte Number | 8-13 |
Rotational Symmetry | none |
Reflection Axes | none |
Palindromic | no |
Chirality | yes enantiomorph: 3885 |
Hemitonia | 5 (multihemitonic) |
Cohemitonia | 3 (tricohemitonic) |
Imperfections | 3 |
Modes | 7 |
Prime? | no prime: 735 |
Deep Scale | no |
Interval Vector | 556453 |
Interval Spectrum | p5m4n6s5d5t3 |
Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4,5} <3> = {3,4,5,6} <4> = {4,5,6,7,8} <5> = {6,7,8,9} <6> = {7,8,9,10} <7> = {9,10,11} |
Spectra Variation | 2.5 |
Maximally Even | no |
Maximal Area Set | no |
Interior Area | 2.616 |
Myhill Property | no |
Balanced | no |
Ridge Tones | none |
Propriety | Improper |
Heliotonic | no |
These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.
* Pitches are shown with C as the root
Triad Type | Triad* | Pitch Classes | Degree | Eccentricity | Closeness Centrality |
---|---|---|---|---|---|
Major Triads | C | {0,4,7} | 4 | 4 | 1.82 |
D♯ | {3,7,10} | 3 | 4 | 2 | |
A | {9,1,4} | 3 | 4 | 2 | |
Minor Triads | cm | {0,3,7} | 3 | 4 | 1.91 |
gm | {7,10,2} | 2 | 4 | 2.27 | |
am | {9,0,4} | 3 | 4 | 1.91 | |
Diminished Triads | c♯° | {1,4,7} | 2 | 4 | 2.09 |
e° | {4,7,10} | 2 | 4 | 2.09 | |
g° | {7,10,1} | 2 | 4 | 2.36 | |
a° | {9,0,3} | 2 | 4 | 2.18 | |
a♯° | {10,1,4} | 2 | 4 | 2.27 |
Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.
Diameter | 4 |
---|---|
Radius | 4 |
Self-Centered | yes |
Modes are the rotational transformation of this scale. Scale 1695 can be rotated to make 7 other scales. The 1st mode is itself.
2nd mode: Scale 2895 | ![]() | Aeoryllic | |||
3rd mode: Scale 3495 | ![]() | Banyllic | |||
4th mode: Scale 3795 | ![]() | Epothyllic | |||
5th mode: Scale 3945 | ![]() | Lydyllic | |||
6th mode: Scale 1005 | ![]() | Radyllic | |||
7th mode: Scale 1275 | ![]() | Stagyllic | |||
8th mode: Scale 2685 | ![]() | Ionoryllic |
The prime form of this scale is Scale 735
Scale 735 | ![]() | Sylyllic |
The octatonic modal family [1695, 2895, 3495, 3795, 3945, 1005, 1275, 2685] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)
The inverse of a scale is a reflection using the root as its axis. The inverse of 1695 is 3885
Scale 3885 | ![]() | Styryllic |
Only scales that are chiral will have an enantiomorph. Scale 1695 is chiral, and its enantiomorph is scale 3885
Scale 3885 | ![]() | Styryllic |
T0 | 1695 | T0I | 3885 | |||||
T1 | 3390 | T1I | 3675 | |||||
T2 | 2685 | T2I | 3255 | |||||
T3 | 1275 | T3I | 2415 | |||||
T4 | 2550 | T4I | 735 | |||||
T5 | 1005 | T5I | 1470 | |||||
T6 | 2010 | T6I | 2940 | |||||
T7 | 4020 | T7I | 1785 | |||||
T8 | 3945 | T8I | 3570 | |||||
T9 | 3795 | T9I | 3045 | |||||
T10 | 3495 | T10I | 1995 | |||||
T11 | 2895 | T11I | 3990 |
These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.
Scale 1693 | ![]() | Dogian | ||
Scale 1691 | ![]() | Kathian | ||
Scale 1687 | ![]() | Phralian | ||
Scale 1679 | ![]() | Kydian | ||
Scale 1711 | ![]() | Adonai Malakh | ||
Scale 1727 | ![]() | Sydygic | ||
Scale 1759 | ![]() | Pylygic | ||
Scale 1567 | ![]() | |||
Scale 1631 | ![]() | Rynyllic | ||
Scale 1823 | ![]() | Phralyllic | ||
Scale 1951 | ![]() | Marygic | ||
Scale 1183 | ![]() | Sadian | ||
Scale 1439 | ![]() | Rolyllic | ||
Scale 671 | ![]() | Stycrian | ||
Scale 2719 | ![]() | Zocryllic | ||
Scale 3743 | ![]() | Thadygic |
This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.
Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO
Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.